Define S(x)=x , _ x ^ x^ 2 e^ t ,dt

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

Define S(x)=x ∫xx2et dt.S(x)=x\,\int_{x}^{x^{2}} e^{t}\,dt. Calculate S′(x)S'(x), expressing your final answer in terms of elementary functions and an integral, if needed.

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